Mechanics of deformation and acoustic propagation in porous media

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Biot, M. A.¹

Mechanics of deformation and acoustic propagation in porous media

J Appl Phys. April 1962;33(4):1482-1498

Affiliations

¹Shell Development Company, Houston, Texas
Abstract

A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid‐solid medium is treated as a complex physical‐chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.
Links

DOI: 10.1063/1.1728759

WoS: A19623774B00006
History

Received: 1961-08-18
Cited Works (1)

Year Entry

1941 Biot MA. General theory of three‐dimensional consolidation. J Appl Phys. February 1941;12(2):155-164.

Cited By (31)

Year	Entry
1970	McElhaney J, Alem N, Roberts V. A porous block model for cancellous bones. Winter Annual Meeting of the American Society of Mechanical Engineers; November 29–December 3, 1970; New York, NY.1-9. ASME Publication 70-WA/BHF-2.
1990	Spilker RL, Suh J-K, Vermilyea ME, Maxian TA. Alternate hybrid, mixed, and penalty finite element formulations for the biphasic model of soft hydrated tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:401-435.
2003	Ateshian GA, Hung CT. Functional properties of native articular cartilage. In: Guilak F, Butler DL, Goldstein SA, Mooney DJ, eds. Functional Tissue Engineering. New York, NY: Inc., Springer-Verlag; 2003:46-68.
1992	Simon BR. Multiphase poroelastic finite element models for soft tissue structures. Appl Mech Rev. June 1992;45(6):191-218.
1991	Suh J-K, Spilker RL, Holmes MH. A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation. Int J Num Meth Eng. November 1991;32(7):1411-1439.
1987	Frank EH, Grodzinsky AJ. Cartilage electromechanics, II: a continuum model of cartilage electrokinetics and correlation with experiments. J Biomech. 1987;20(6):629-639.
1994	Ateshian GA, Lai WM, Zhu WB, Mow VC. An asymptotic solution for the contact of two biphasic cartilage layers. J Biomech. November 1994;27(11):1347-1360.
1994	Deligianni DD, Maris A, Missirlis YF. Stress relaxation behaviour of trabecular bone specimens. J Biomech. December 1994;27(12):1469-1476.
1995	Kim Y-J, Bonassar LJ, Grodzinsky AJ. The role of cartilage streaming potential, fluid flow and pressure in the stimulation of chondrocyte biosynthesis during dynamic compression. J Biomech. September 1995;28(9):1055-1066.
1995	Ateshian GA, Wang H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. J Biomech. November 1995;28(11):1341-1355.
1985	Simon BR, Wu JSS, Carlton MW, Evans JH, Kazarian LE. Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk. J Biomech Eng. November 1985;107(4):327-335.
1987	Eisenberg SR, Grodzinsky AJ. The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma. J Biomech Eng. February 1987;109(1):79-89.
1990	Spilker RL, Suh J-K, Mow VC. Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis. J Biomech Eng. May 1990;112(2):138-146.
1992	Spilker RL, Suh J-K, Mow VC. A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. J Biomech Eng. May 1992;114(2):191-201.
1996	Kelkar R. Normal and Abnormal Mechanics of the Shoulder: Studies of Articular Geometry, Contact and Kinematics [PhD thesis]. Columbia University; 1996.
1997	Wang X. The Frictional Role of Interstitial Fluid Viscosity At the Interface of Deformable Porous Media [PhD thesis]. Columbia University; 1997.
1997	Wang H. Boundary Lubrication of Articular Cartilage: The Role of Interstitial Fluid Pressure, Surface Porosities and Equilibrium Friction Coefficient [PhD thesis]. Columbia University; 1997.
2002	Sun D. Theoretical and Experimental Investigations of the Mechano-Electrochemical Properties of Articular Cartilage, a Charged -Hydrated -Soft, Biological Tissue [PhD thesis]. Columbia University; 2002.
2013	Souzanchi MF. The Effect of Microarchitecture and Fabric Anisotropy of Trabecular Bone on Its Mechanical Behavior [PhD thesis]. New York, NY: The City University of New York; 2013.
2002	Dupont T. Transparence et absorption acoustiques des structures microperforées [Sound Transmission and Absorption of Microperforated Structures] [PhD thesis]. Institut national des sciences appliquées de Lyon (INSA Lyon); 2002.
1987	Sachs JR. A Mathematical Model of an Electromechanically Coupled Poroelastic Medium [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 1987.
2016	Young WT. Cartilage Stress Relaxation Induced by Intra-Tissue Transport of Cationic Nanoparticles: Implications for Post-Traumatic Osteoarthritis Drug Delivery [Master's thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 2016.
2002	Wang X. Simulation for Bone Adaptive Remodeling: A Stochastic Approach With Application on Spine Fusion [PhD thesis]. Queen's University; May 2002.
1989	Suh J-K. A Finite Element Formulation for Nonlinear Behavior of Biphasic Hydrated Soft Tissues Under Finite Deformation [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; September 1989.
2019	Rahimi A. Simulation of the Acoustic Pressure Field and Study of Cellular Responses of Osteoprogenitors Using Low-Intensity Pulsed Ultrasound Treatment in an in Vitro Ultrasound Bioreactor [PhD thesis]. St. Louis, MO: Saint Louis University; 2019.
2001	Lin W. Development of Quantitative Ultrasound to Determine the Physical Properties of Bone [PhD thesis]. Stony Brook, NY: State University of New York at Stony Brook; May 2001.
2006	Rouhi G. Theoretical Aspects of Bone Remodeling and Resorption Processes [PhD thesis]. Calgary, AB: University of Calgary; March 2006.
1990	Wayne JS. Application of the u-p Finite Element Method to the Study of Articular Cartilage Under Small and Large Strains [PhD thesis]. San Diego (UCSD), University of California; 1990.
2018	Jafari S. Biomechanics of Articular Cartilage: Osteoarthritis and Tissue Engineering [PhD thesis]. San Diego (UCSD), University of California; 2018.
1991	Hale JE. Some Aspects of the Biomechanics of Local Articular Incongruities [PhD thesis]. University of Iowa; December 1991.
1995	Grimm MJ. Ultrasound Propagation Through the Calcaneus: Dependence on “Bone Quality” and Prediction by Biot's Theory [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1995.